Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

 Quantlet: spcewma1ad Description: Computes the Average Delays of a one-sided EWMA chart for a given critical value and for various expected values mu. The data is normally distributed with variance 1.

Reference(s):
Lucas, J.M. and Saccucci, M.S. (1990). Exponentially Weighted Moving Average Control Schemes: Properties and Enhancements. Technometrics: 32. pp. 1-12. Roberts, S.W. (1959). Control Chart Tests Based on Geometric Moving Averages. Technometrics: 1. pp. 239-250.

 Usage: ad = spcewma1ad (mu, lambda, c, zreflect,r) Input: mu n x 1 vector representing the expected values of the user-defined random variable lambda scalar, containing the smoothing parameter c scalar, critical value zreflect scalar representing a pre-defined border. It is usually less than zero. If zreflect is small enough, ARL and AD of the bounded scheme are the same as of the unbounded. r scalar, matrix dimension of the approximating one-dimensional Markov chain Output: ad n x 1 vector of scalars containing the average delays of a one-sided EWMA chart

Note:
The algorithm is based on the Brook/Evans approach. At zreflect<=0 the EWMA statistic is reflected, i.e., the continuation region (-infinity,c] is truncated into (zreflect,c].

Example:
```; ADs of a one-sided EWMA chart for different expected values
; mu, smoothing parameter lambda = 0.5 and matrix dimension 50
;(of the approximating one-dimensional Markov chain):
library("spc")
mu =(0:4)/4
c = spcewma1c(100,0.5,-4,50)

```
Result:
```Contents of _tmp
[1,]        0   99.398
[2,]     0.25   38.577
[3,]      0.5   18.043
[4,]     0.75   9.9513
[5,]        1   6.2833
```

Author: S. Knoth, 20011010 license MD*Tech
(C) MD*TECH Method and Data Technologies, 05.02.2006